The use of the heat operator in an existence theory problem of the Vlasov equation. (English) Zbl 0595.76126

(Author’s summary.) A use is demonstrated for a parabolic operator in the context of the existence theory problem of the Vlasov-Poisson systems. It is shown that some aspects of the evolution of the field can be viewed as a diffusion process and that relevant estimates on the field can be derived through the use of the heat operator. The application of this to the existence theory problem is demonstrated.
Reviewer: J.Blum


76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanics of plasmas
35Q99 Partial differential equations of mathematical physics and other areas of application
46N99 Miscellaneous applications of functional analysis
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